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In the physical world, one cannot increase the size or quantity of anything without changing its quality. Similar figures exist only in pure geometry.
Emotions are far harder things to understand than algebra and geometry, yet we spend hours in elucidating mathematics and expect such a problem as that of human relationships to solve itself.
Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.
Perhaps you have seen me. I know well, my purpose was merely that of a symbol, 'equals', 'times'... ; but what is said, for all that, was identity-less: a kind of live geometry.
What physics tells us is that everything comes down to geometry and the interactions of elementary particles. And things can happen only if these interactions are perfectly balanced.
Or maybe it is only that we are so habitually inattentive that when some rare but simple geometry grabs us by the shoulders and shakes us into consciousness, we call our response sacred.
I find that I never lose Bach. I don't know why I have always loved him so. Except that he is so pure, so relentless and incorruptible, like a principle of geometry.
You must follow me carefully. I shall have to controvert one or two ideas that are almost universally accepted. The geometry, for instance, they taught you at school is founded on a misconception.
Now, a 45-degree angle is not something we deal with in finance. It's something you see in a high school geometry class. Performance like that has never been recorded in human history.
Really, universally, relations stop nowhere, and the exquisite problem of the artist is eternally but to draw, by a geometry of his own, the circle within which they shall happily appear to do so.
For each successive class of phenomena, a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature.
It [ non-Euclidean geometry ] would be ranked among the most famous achievements of the entire [nineteenth] century, but up to 1860 the interest was rather slight.
I can't stop biting my nails. It's a bad habit of mine. I like anything to do with math and numbers. I know a lot of people don't like geometry, but for me it's fun.
..if a special geometry has to be invented in order to account for a falling apple, even Newton might be appalled at the complications which would ensue when really difficult problems are tackled.
In the morning a man walks with his whole body; in the evening, only with his legs. RALPH WALDO EMERSON, Journals and Miscellaneous Notebooks Greek architecture is the perfect flowering of geometry.
The opinions of men should not be the object of any government. Our civil rights are no more dependent on our religious beliefs than they are dependent upon our thoughts about geometry or physics!